It’s the day after the last day of what has been a very busy semester. Being busy is good, and being awash in new information every day is something I relish. But there comes a time when we must pause and reflect, and too often this semester I have not given myself that time. Admittedly, just keeping up with the flood of new information proved to be too much, and the student-to-student whispers of “You can’t read everything, you know” proved too regularly to be true. But finally, now, I can take a few hours and think about the last core course of my doctoral program: Multicultural Education (MCED), taught by Linda Mizell.

Assessing the value of this class has been difficult, as there were plenty of moments during the semester when I felt I wasn’t making much scholarly progress. One reason for that feeling – and a reason I appreciate – is that prior coursework had left me better prepared for MCED than I expected. (Or so I thought.) Rarely were the issues we explored in MCED not ones I’d considered in prior courses like Culture and Ethnography, Ethics in Education, Policy Issues, Education Research and Policy, and Perspectives on Classrooms, Teaching, and Learning. It is a credit to my institution that attention to multiculturalism and equity permeates into most corners of the school, although I admit there are times where I still sense it as artificially layered on to a lesson or, even worse, uncomfortably absent. A second reason for that lack-of-progress feeling stemmed from not being able to keep up with all the reading and assignments for the semester. As I finished the last of my papers last night, I thought back to what remained unfinished and one reading in particular stood out: Eduardo Bonilla-Silva’s Racism Without Racists.

So after submitting my last final paper, I pulled Bonilla-Silva back off the shelf and picked up where I’d left off. I had read all but the last two chapters, but it was in those last two chapters where things appeared to get most interesting. In this, the third edition of Racism Without Racists, Bonilla-Silva added a new chapter at the end addressing the “Obama Phenomenon.” I started reading and almost immediately I was taken back to what I thought made this book so interesting, engaging, and challenging to begin with: Bonilla-Silva’s outspoken criticism of a system that perpetuates racism and inequality. In general, I do not disagree with Bonilla-Silva’s message. But the style with which the message was delivered came as a bit of an uncomfortable shock.

In his detailed analysis of interviews with both white and minority students, Bonilla-Silva exposed the racism found in peoples’ language. For example, in an interview with a white girl named Jill who claimed, “One of my best friends is black” (p. 58), Bonilla-Silva asks her to go into more detail. Jill then describes her friend as “bright” but with “terrible GMAT scores,” and then says, “What he lacks in intellect he makes up for in…he works so hard and he’s always trying to improve himself.” In his analysis, Bonilla-Silva addresses the contradiction about intelligence and points out that Jill never mentions this friend by name. This example by itself might seem lacking in evidence, but it is far from an isolated incident in the text. The dissection of racism in peoples’ speech happens on page after page. Sometimes it’s subtle, sometimes less so, and I remember feeling during my first reading that I’m glad Bonilla-Silva wasn’t interviewing me, because he seemed to make everybody sound racist!

Now, reflecting exactly on that thought, I see how that thinking exposes how I largely missed Bonilla-Silva’s greater point (even though it’s the title of the book): the kind of racism we’re dealing with now is less about the individual and more about a system. Bonilla-Silva wasn’t after Jill to make her sound like a racist – at least not the kind of racist most people imagine when they hear that label. Bonilla-Silva was instead exposing how Jill, along with most of the other interviewees in the book, demonstrates the systems and structures of racism and how they exist in what we all say, do, and believe. In other words, it’s not about Jill. For the same reason, I shouldn’t have worried about Bonilla-Silva interviewing me, as the interview would have only helped me understand how my actions, behaviors, and attitudes are being affected by the subtle yet significant culture of racism that still exists in our society. And until we are forced to recognize it, there is very little we can or will do about it.

It’s also this same system that allowed much of the country to endorse President Obama, and how that endorsement gives us a false sense of accomplishment that we’ve somehow reached a “post-racial” society. (We haven’t.) As an educator I wonder how we can have policies like NCLB which are so bold to declare a school a failure when achievement gaps persist, yet our greater society and government doesn’t always extend that same failure judgment to the enormous gaps in achievement, income, wealth, health, etc. that we see in our society. Sure, the #Occupy protesters have their message, but it’s unfortunate that so few were shouting until the perils of inequity reached beyond minorities.

The system that Bonilla-Silva describes should not have been an “uncomfortable shock” to me. From where I now stand, I can see how other readings described much of the same system, yet somehow by using more academic or less forceful language I was led to think I understood when I didn’t. Perhaps the best example of this is Beverly Daniel Tatum’s book “Why Are All the Black Kids Sitting Together in the Cafeteria?” I remember thinking as I read it, “I really like Beverly Daniel Tatum because she’s making me feel comfortable about a difficult topic.” Where I feared an interview with Bonilla-Silva, I would have welcomed the opportunity to speak with Beverly Daniel Tatum.

But somehow, disguised by my initial affection for the authors, I didn’t immediately see how in many ways Bonilla-Silva and Tatum were largely describing the same system of racism. I’m glad I read Tatum first and then Bonilla-Silva, because now as I reflect I can see how Tatum’s message didn’t really sink in for me; if it had, I wouldn’t have been so challenged by Bonilla-Silva. The lesson for me is not that I need to keep reading more critical work (although that would certainly help), but that it’s going to take more effort to make myself feel uncomfortable about issues of culture, race, class, power, etc., before somebody else gets the chance to do it for me.

For me, the simple title to this post has a double meaning. First is the more obvious, that I’m finally taking some time to think about a class I experienced over the past semester. Second, and more importantly, is the idea that multicultural education has a reflective property like a mirror bouncing light around a corner. As an educator who had a relatively monocultural upbringing in the rural Midwest, and who apparently can still be surprised by the injustices in the world around me, I need to use what I’ve learned about multicultural education to shine some light not only around corners, but back on myself. There’s so much more for me to see, most of which is hidden by its largeness, not its smallness. As an educator this is what we do: we help students explore and understand the world around them, and our reward for doing so comes both in our students’ growth and our own.

Many teachers who choose to use standards-based grading eventually find themselves facing the reality of their school's grading policies and tradition: the expectation of final, summative grades that are reported as percentages and letters. So regardless how hard you try to focus on quality feedback instead of grades all semester long (for good reason), there comes a time when, for reasons probably beyond your control, you have to turn levels and descriptions of student understanding into numbers. This is SBG's "Monday Morning Problem" that doesn't always get addressed in theory. But this week is finals week for my basic statistics students, so for me the time has come to convert standards-based formative grades into a summative grade, including calculating final exam grades. Here I'll try to describe the two steps I'll take to calculate my students' grades: (a) conversion of their formative scores into a summative score and (b) scoring and inclusion of the final exam into their semester grades.

Formative to Summative
Besides giving students a lot of written and verbal feedback about where they should try to improve, I've been using the simplest of measures to record their performance on class objectives: either students (a) "get it," (b) "sort of get it," or (c) "dont' get it/haven't demonstrated it." You could think of these as "green light," "yellow light," and "red light," respectively. I've tried discerning more levels of understanding in a gradebook and it only seems to lead to confusion and indecision (both for me and students), so I'm sticking to three levels, as suggested in Her & Webb (2004). If I need more detail, I can always go back to the copies of the work students have submitted and the comments I've made.

The gradebook we have for class is pretty primitive and as far as I can tell it only accepts numbers, so I mark my three levels as either a 2, a 1, or a 0. It doesn't take much explaining to students that a 1 shouldn't be viewed as "out of two" and therefore worth 50%. I do tell them, though, that in order to receive credit for the course they should average a 1 across all objectives. In other words, you can't pass the class without an average of at least some understanding of every objective.

Around here and in many other places, 70% seems to be the low end of passing grades. (We're not messing with Ds.) So if a student with all 1s should get at least a 70%, and a student with all 2s maxes out at 100, and we choose a linear function between the two, the "conversion formula" to percentages is simply:

percentage = 30 * objective score average + 40

If you feel a little dirty at this point because you know you just reduced all the various skills, knowledge, and abilities of your students into a single number, I say join the club. If you didn't feel that way I wouldn't have expected you to be using standards-based grading to begin with.

A "No Surprises" Approach to Final Exam Grades
Designing a final exam is often tricky business. It can't possibly assess everything in the course, but we generally want it to include the major topics and themes for the class and be possible to complete in the time allowed. We also have to think about difficulty. Trust me, your students are!

Teachers want their finals to be challenging, but they don't want to have that sinking feeling as they grade the exams that maybe the test was too hard. For whatever reason, sometimes students perform poorly and averaging the final exam grade into their other grades will look like a disaster. But ask yourself: What am I more confident in, my careful judgments of students' ability as demonstrated over an entire semester, or a fleeting, one-time judgement of students' ability on a single assessment during the most stressful time of the year? If you're using standards-based grading, I already know how you'll answer that question. If not, consider this example: I have a student who I know can do stats. She's turned in good work. She's asked quality questions. We've had good discussions. But I also know she has seven final exams this week. I still think she'll do fine, but I'll understand if she's not at her best. And I need a grading system that reflects that understanding.

In order to free myself to still give challenging, yet reasonable, assessments, without risking any huge surprises when grades are calculated, I perform a little statistical magic that ensures that the distribution of final grades has the same center and spread of class grades before the final. I'm sure many of you try "curving" your exam scores some other way, such as letting the top score count as the total possible, or even having a pre-set distribution in mind of how many As, Bs, Cs, etc. you'll allow (which is not a good idea, generally, for reasons described by Krumboltz & Yeh, 1996). I prefer my method because it accounts for the distribution of grades, not just the top score, and the distribution is determined by the students, not arbitrarily by me. Allow me to demonstrate with a couple examples.

Suppose before the final the average percentage grade is 85 and the standard deviation of those grades is 10. Then I grade my final exams and find that the average final exam grade is 60 with a standard deviation of 18. Ouch. But don't worry -- statistics will come to our rescue.

Provided you know a little basic descriptive statistics, the conversion is simple. For each student's final exam score, find out how many standard deviations above or below the mean they scored on the final (their final exam z-score), and match that with the same number of standard deviations above or below the mean they'd fall on the pre-final grade distribution (their pre-final z-score). Consider the following students and the class and exam statistics above:

Suppose Student A scores a 51 on the final exam. That's 0.5 standard deviations below the mean. (51 - 60 = -9, and -9/18 = -0.5.) So where is 0.5 standard deviations below the mean on the pre-final distribution? If that mean is 85 and the SD is 10, then 0.5 standard deviations below the mean is 80. So I record an 80 for that student instead of a 51.

Suppose Student B scores a 75 on the final exam. That's about 0.83 standard deviations above the mean. (75 - 60 = 15, and 15/18 = 0.83.) So where is 0.83 standard deviations above the mean on the pre-final distribution? About 8.3% above an 85, so I record their exam grade as a 93.3.

Suppose Student C scores a 60 on the final exam. That's the same as the mean, so zero standard deviations above or below. That conversion is super-easy: their final exam grade is the mean of the pre-final mean, an 85.

This is not a perfect system (and comments about its imperfections are welcome in the comments), but it does take away the element of surprise if the final exam happens to be way too easy or too difficult, or if other circumstances prevent grades from working out the way you'd expect. Yes, this is a norm-referenced system instead of a criterion-referenced system, meaning that the grades students earn on the final is measured largely as how they compare to their classmates and the class average. The good news is this: both the teacher and the students have an incentive before the final to master as many objectives as possible, and that is criterion-referenced. A high pre-final average helps everyone get a high final exam average, and a small pre-final standard deviation minimizes variability in final exam scores.